Peter Koepke

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Using the core model K we determine better lower bounds for the consistency strength of some combinatorial principles: I. Assume that A is a Jonsson cardinal which is ‘accessible’ in the sense that at least one of (l)-(4) holds: (1) A is a successor cardinal; (2) A = oE and 6 <A ; (3) A is singular of uncountable cofinality; (4) A is a regular but not(More)
We define the notion of ordinal computability by generalizing standard Turing computability on tapes of length ω to computations on tapes of arbitrary ordinal length. We show that a set of ordinals is ordinal computable from a finite set of ordinal parameters if and only if it is an element of Gödel’s constructible universe L. This characterization can be(More)
Scattering functions, i.e., the scattered intensity as a function of angle, are modeled for tropospheric aerosol types with respect to the effect of the nonspherical shape of the particles. Scattering functions of nonspherical particles compared with those of equivalent spheres show differences increasing with particle size. Thus, for aerosol types with a(More)
We generalize standard Turing machines working in time ω on a tape of length ω to abstract machines with time α and tape length α, for α some limit ordinal. This model of computation determines an associated computability theory: α-computability theory. We compare the new theory to α-recursion theory, which was developed by G. Sacks and his school. For α an(More)
The Naproche project (NAtural language PROof CHEcking) studies the semiformal language of mathematics (SFLM) as used in journals and textbooks from the perspectives of linguistics, logic and mathematics. A central goal of Naproche is to develop and implement a controlled natural language (CNL) for mathematical texts which can be transformed automatically(More)
Infinite time register machines (ITRMs) are register machines which act on natural numbers and which may run for arbitrarily many ordinal steps. Successor steps are determined by standard register machine commands, at limits the register contents are defined as lim inf’s of the previous register contents. We prove that a real number is computable by an ITRM(More)